1. Field of the Invention
The subject matter disclosed herein relates generally to the field of kernel regression modeling used for forecasting of financial time series data, and more particularly to the use of multivariate kernel regression models for forecasting of correlated financial parameters.
2. Brief Description of the Related Art
Kernel regression is a form of modeling used to determine a non-linear function or relationship between values in a dataset and is used to monitor machines or systems to determine the condition of the machine or system. One known form of kernel regression modeling is similarity-based modeling (SBM) disclosed by U.S. Pat. Nos. 5,764,509 and 6,181,975. For SBM, multiple sensor signals measure physically correlated parameters of a machine, system, or other object being monitored to provide sensor data. The parameter data may include the actual or current values from the signals or other calculated data whether or not based on the sensor signals. The parameter data is then processed by an empirical model to provide estimates of those values. The estimates are then compared to the actual or current values to determine if a fault exists in the system being monitored.
More specifically, the model generates the estimates using a reference library of selected historic patterns of sensor values representative of known operational states. These patterns are also referred to as vectors, snapshots, or observations, and include values from multiple sensors or other input data that indicate the condition of the machine being monitored at an instant in time. In the case of the reference vectors from the reference library, the vectors usually indicate normal operation of the machine being monitored. The model compares the vector from the current time to a number of selected learned vectors from known states of the reference library to estimate the current state of the system. Generally speaking, the current vector is compared to a matrix made of selected vectors from the reference library to form a weight vector. In a further step, the weight vector is multiplied by the matrix to calculate a vector of estimate values. The estimate vector is then compared to the current vector. If the estimate and actual values in the vectors are not sufficiently similar, this may indicate a fault exists in the object being monitored.
However, this kernel regression technique does not explicitly use the time domain information in the sensor signals, and instead treats the data in distinct and disconnected time-contemporaneous patterns when calculating the estimates. For instance, since each current vector is compared to the reference library vectors individually, it makes no difference in what order the current vectors are compared to the vectors of the reference library—each current vector will receive its own corresponding estimate vector.
Some known models do capture time domain information within a kernel regression modeling construct. For example, complex signal decomposition techniques convert time varying signals into frequency components as disclosed by U.S. Pat. Nos. 6,957,172 and 7,409,320, or spectral features as disclosed by U.S. Pat. No. 7,085,675. These components or features are provided as individual inputs to the empirical modeling engine so that the single complex signal is represented by a pattern or vector of frequency values that occur at the same time. The empirical modeling engine compares the extracted component inputs (current or actual vector) against expected values to derive more information about the actual signal or about the state of the system generating the time varying signals. These methods are designed to work with a single periodic signal such as an acoustic or vibration signal. But even with the system for complex signals, the time domain information is not important when calculating the estimates for the current vector since each current vector is compared to a matrix of vectors with reference or expected vectors regardless of the time period that the input vectors represent.